A method for the measurement and interpretation of neuronal interactions: improved fitting of cross-correlation histograms using 1D-Gabor Functions

Cross-correlation analysis of separable multi-unit activity is the most used method to investigate neuronal connectivity. Features such as peaks, troughs, and satellite peaks in the cross-correlogram reflect the temporal relation between the activities of neurons. Precise estimation of such features requires independent measures. A very popular and effective method is to perform curve fitting using 1D Gabor functions. However, because of the non-linearity of the function, an iterative fitting procedure using optimization algorithms is required. As proposed from literature, we used the Levenberg-Marquardt algorithm. However, when applied to our data, the algorithm performed poorly. Here, we show that Trust Region algorithm represent a more attractive alternative to Levenberg-Marquardt in terms of performance and computational cost.